Circle A has a radius of #2 # and a center at #(3 ,6 )#. Circle B has a radius of #5 # and a center at #(2 ,3 )#. If circle B is translated by #<-2 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
What we have to do here is compare the distance (d) between the centres of the circles to the sum of the radii.
• If sum of radii > d , then circles overlap
• If sum of radii < d , then no overlap
The first step is to find the new centre of B under the translation. A translation does not change the shape of a figure , only it's position.
Under a translation of
centre B(2 ,3) → (2-2 ,3+1) → B(0 ,4)-(new centre)
To calculate the distance (d) between the centres use the
#color(blue)" distance formula"#
# (x_1,y_1)" and " (x_2,y_2)" are 2 points"#
The 2 points here being the centres of A and B.
# (x_1,y_1)=(3,6)" and " (x_2,y_2)=(0,4)#
radius of A + radius of B = 2 + 5 = 7
Since sum of radii > d , then circles overlap.